5 citations · 8 across the 6 of their papers we have counts for
6 papers
Weak solutions of 3D compressible Navier-Stokes equations in critical case
Pavel I. Plotnikov
New estimates of the potentials of solutions to the compressible Navier-Stokes equations are derived. The result obtained are applied to boundary value problems for the compressibl…
A Proof of Hélein's Conjecture on Boundedness of Conformal Factors when n=3
P. I. Plotnikov, J. F. Toland
For smooth mappings of the unit disc into the oriented Grassmannian manifold , Hélein (2002) conjectured the global existence of Coulomb frames with bounded confor…
Kolmogorov's Theorem for Low-Dimensional Invariant Tori of Hamiltonian Systems
Pavel Plotnikov, Ivan Kuznetsov
In this paper the problem of persistence of invariant tori under small perturbations of integrable Hamiltonian systems is considered. The existence of one-to-one correspondence bet…
Isothermal Navier-Stokes Equations and Radon Transform
P. I. Plotnikov, W. Weigant
In the paper we prove the existence results for initial-value boundary value problems for compressible isothermal Navier-Stokes equations. We restrict ourselves to 2D case of a pro…
Steady 3D viscous compressible flows with adiabatic exponent
P. I. Plotnikov, W. Weigant
The Navier-Stokes equations for compressible barotropic flow in the stationary three dimensional case are considered. It is assumed that a fluid occupies a bounded domain and satis…
Small divisor problem in the theory of three-dimensional water gravity waves
Gérard Iooss, Pavel I. Plotnikov
We consider doubly-periodic travelling waves at the surface of an infinitely deep perfect fluid, only subjected to gravity and resulting from the nonlinear interaction of two s…